F0- and F1-transforms; nonlocal operators; nonlocal operators; nonlocal Laplacean

In nonlocal operators, nonlocal operators define a new type of functionals that extend the ability of classical PDE-based algorithms in handling textures and repetitive structures. We showed that in the particular space with a fuzzy partition, the nonlocal Laplacean and partial derivatives can be represented by the F0- and F1-transforms. For the restoration problem specified by relatively large damaged areas, we propose a new total variation model with the F-transform-based nonlocal operators. We show that the proposed model together with the corresponding algorithm increase the quality of a (usually considered) patch-based searching algorithm.